Which are the remote interior angles of the exterior 1?

What are the remote and interior angles?

It's all about extending a side of the triangle

An exterior angle of a triangle, or any polygon, is formed by extending one of the sides.

In a triangle, each exterior angle has two remote interior angles . The remote interior angles are just the two angles that are inside the triangle and opposite from the exterior angle.

The Formula

As the picture above shows, the formula for remote and interior angles states that the measure of a an exterior angle $$ \angle A $$ equals the sum of the remote interior angles.

To rephrase it, the angle 'outside the triangle' (exterior angle A) equals D + C (the sum of the remote interior angles).

If one side of a triangle is extended beyond the vertex, an exterior angle is formed. This exterior angle is supplementary with its adjacent, linear angle. Since the angle sum in a triangle is also 180 degrees, the exterior angle must have a measure equal to the sum of the remaining angles, called the remote interior angles.

When we talk about exterior angles and the remote interior angles it helps that we think about what in English what do they mean do they mean? Exterior means outside, so this is angle 1 outside of our triangle. The angles that are inside the triangles are the interior but there's only two that are remote. Remote means far away which is why when you're trying to use your TV you use a remote because your far away, so the remote interior angles are 3 and 4 so again 1 is your exterior angle because it's outside and the two angles that are not adjacent to angle 1 are your remote interior angles.
There's a special relationship that exists here and that is angle 1 is equal to angle 3 plus angle 4 but you're not just going to take my word for it you're going say "Mr. McCall you need to prove that," so what I'm going to do is I'm going to say angle 1 and angle 2 must sum to 180 degrees because if I add those two angles up we get a straight line. The second thing I'm going to say is that these 3 angles 2, 3, 3. 2, 3 and 4 must sum to 180 degrees because they make a triangle.
If I solve this equation for 2, I'm sorry that 2 is a little messy, then I can substitute in to my first equation, so I'm going to subtract angle 3 and I'm going to subtract angle 4 so what I'm doing is just moving everything to the other side of that equation so subtract angle 3 subtract angle 4 and I find that angle 2 must equal 180 minus those two angles, so 180 degrees minus angle 3 minus angle 4 so I know angle 2 in terms of angle 3 and 4 and I'm going to substitute that in right over there, so we're going to shift and I'm going to say angle 1 plus angle 2 which we said was 180 minus angle 3 minus angle 4 if we go back to our original equation here that has to equal 180 degrees. I see I have 180 degrees on both sides so I'm just going to minus 180 and then that will make them disappear and if I move negatives angle 3 and negative angle 4 to the other side by adding angle 3 and angle 4 then all I have left is angle 1 is equal to 180 and negative 180 is 0 so we have angle 3 plus angle 4 which has proven that the remote exterior angle excuse me the exterior angle is equal to the sum of the remote interior angles.

The measure of an exterior angle can be found with the values of the remote interior angles. The remote interior angles are the angles inside of the triangle that are not adjacent to the desired exterior angle.

This exterior angle's measure is the sum of the remote interior angle). This is because from the triangle angle sum theorem that the sum of the angles inside a triangle is 180°, and the sum of a linear pair (two adjacent angles that lie on the same line) is also 180°. As a result, since the adjacent interior angle is 180° - the sum of the remote interior angles, and it is also 180° - the exterior angle, the measure of the exterior angle is the same as the sum of the remote interior angles.

We can use remote interior angles to find missing angles. So if we look here x is an exterior angle and 90 degrees and 35 are the more interior angles.

So let’s start by saying x degrees must equal 90 plus 35. Well, that’s pretty simple. 90 and one 35, is 125. So I can erase x and I know that this is 125 degrees. To find y, I can say that 125 and y must be a linear pair or supplementary, which means y plus 125 equals 180 degrees. So we’ll subtract 125 degrees from both sides and we see that y has to be 55 degrees.

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< = angle

An exterior angle is formed between a side and the extension of a side. It will always be a linear pair with an internal angle. In the diagram below, <4 is the exterior angle. The exterior angle theorem states that the external angle is equal to the sum of the two remote angles. The remote angles are those interior angles that are not adjacent to the exterior angle so in this case <1 and <2 are the remote angles.

m<1 + m<2 = m<4, Explain why this is true please !!

asked Sep 30, 2015 at 21:19

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1

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Angle $1$ + Angle $2$ + Angle $3$ = 180

Angle $3$ + Angle $4$ = 180.

The result is that Angle $4$ = Angle $1$ + Angle $2$.

answered Sep 30, 2015 at 21:22

Oria GruberOria Gruber

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Which are the remote interior angles of the exterior angle 1?

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What is the measure of 1 exterior angle?

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